CN106844935A - A kind of big damping engineering structure Modal Parameters Identification - Google Patents

Abstract

The invention belongs to monitoring structural health conditions field, relate generally to damp engineering structure Modal Parameters Identification greatly.The present invention is transformed into frequency domain by by the cross-correlation function of structural vibration response under arbitrary excitation, independent component analysis are carried out so as to real part or imaginary part that frequency domain data can be used to obtain Mode Shape and modal response, and rough modal frequency and damping ratio further is tried to achieve using Fast Fourier Transform (FFT) and half-power bandwidth method to each rank modal response, then as the initial value of modal response curve matching, each rank modal response is fitted using least-squares iteration method respectively, finally can obtain the exact value of each rank modal frequency and damping ratio.The invention can make the data after treatment meet the independence assumption of independent component analysis, can accurately identify the modal parameter of big damping structure.

Description

A kind of big damping engineering structure Modal Parameters Identification

Technical field

The invention belongs to structural health monitoring technology field, it is related to engineering structure Modal Parameters Identification, specially one Plant big damping engineering structure Modal Parameters Identification.

Background technology

The Modal Parameter Identification of engineering structure occupies an important position in monitoring structural health conditions, accurately identifies the mould of structure State parameter (frequency, the vibration shape and damping ratio) is particularly important for Damage Assessment Method and Performance Evaluation.The mode ginseng of engineering structure Number recognition methods is broadly divided into time domain, frequency domain and time-frequency domain three major types.Independent component analysis method is the one of new proposition in recent years Signal procesing in time domain method is planted, has been successfully applied in the Modal Parameter Identification of structure.The method merely with structure when Domain response data, just can obtain the Mode Shape and modal response of structure, and can further obtain frequency and the damping of structure Than.However, due to the presence of the big damping of some engineering structures so that the modal response of structure is more difficult to meet independent component analysis Independence assumption, causes independent component analysis method to accurately identify the modal parameter of big damping structure.

Regarding to the issue above, it is main at present that time domain data is transformed to and using inverse by time-frequency domain using Short Time Fourier Transform Damping becomes the response that big damping structure response of changing commanders is converted into approximate small damping, although these method for transformation can be to a certain degree The upper independent component analysis that improve recognize the accuracy of big damping structure modal parameter, but have ignored the basic vacation for meeting independence If causing recognition result that there is certain approximation.Therefore, using certain method, the application model of independent component analysis is expanded Enclose, there is important engineering significance in the accuracy of engineering structure Modal Parameter Identification for improving the method.

The content of the invention

It is an object of the invention to provide a kind of big damping engineering structure Modal Parameters Identification, independent component analysis are solved Method can not accurately identify the problem of big damping structure modal parameter.

The present invention derives a kind of frequency domain independent component analysis method, is characterized in the thought based on natural excitation method, tries to achieve The cross-correlation function of structural vibration response under arbitrary excitation, as free vibration response, will using Fast Fourier Transform (FFT) The cross-correlation function for obtaining transforms from the time domain to frequency domain, so that meeting independence between each component；Exist according to vibration shape matrix The characteristics of keeping constant in linear transform process, and then the frequency domain data that will be obtained is used as the process object of independent component analysis, Separation matrix and Mode Shape are obtained, each rank free damping mould of time domain is obtained further with cross-correlation function and separation matrix State is responded；Then, obtain each rank free damping using Fourier transformation and half-power bandwidth method and respond rough frequency and damping Than and as initial value, and carrying out optimal estimating to the parameter of exponential damping resonance curve using least-squares iteration method Meter, finally gives each accurate frequency of rank mode and damping ratio.

Technical scheme：

A kind of big damping engineering structure Modal Parameters Identification, step is as follows：

Step one：Calculate Mode Shape matrix

(1) vibration response signal y (t)=[y of structure is gathered₁(t),y₂(t),…,y_k(t)]^T, wherein k is sensor Number；Select a certain signal y_jAs reference, the cross-correlation function matrix r of each components of y (t) is obtained_y(t)；

(2) to r_yT () enters line translation, obtain the plural numeric field data R of frequency domain_y(ω), following form：

R_y(ω)=R_Re(ω)+iR_Im(ω)

Take R_yThe real part R of (ω)_Re(ω) or imaginary part R_Im(ω)；

(3) by R_Re(ω) or R_Im(ω) obtains separation matrix D as analysis object, solves the inverse matrix D- of D¹, shaken Type matrix A=D-¹；

(4) according to step (1) and step (3), modal response matrix is calculated：

S (t)=Dr_y(t)

In formula：S (t) is free damped modal response, and S (t)=[s₁(t),s₂(t),…,s_l(t)]^T, D is separation Matrix, r_yT () is cross-correlation function matrix, l is rank number of mode；

Step 2：Calculate each rank modal frequency and damping ratio

(5) to jth rank modal vector s_jT () implements conversion, and pick up damping vibrition frequencies omega_0dj, try to achieve modal damping Compare ζ_0j, wherein j=[1,2 ..., l]；

(6) jth rank modal response s_jT the theoretical expression of () is：

According to step (5) and relational expressionProvide s_jEach parameter ω in (t)_nj、ω_djAnd ζ_j's Initial value ω_0nj、ω_0djAnd ζ_0j, and by factor alpha_jAnd phaseInitial value be taken as constant, wherein j=[1,2 ..., l] respectively.

(7) estimate of jth rank modal response is：

Wherein：WithRepresentThe estimate of middle parameters.The plan of modal response Closing error is：

Wherein：||·||₂Represent 2- norms.E will be minimized as target, and be calculated according to step (6) Initial value, obtain s_jT the optimal estimation of parameter in (), finally gives each rank natural frequency ω_nj, damped frequency ω_djAnd resistance Buddhist nun compares ζ_j。

Beneficial effects of the present invention：With good noise immunity, the data after conversion meet the independence of independent component analysis Property for big damping structure and small damping structure it is assumed that can accurately obtain modal parameter.

Specific embodiment

Below in conjunction with technical scheme, the implementation method that the present invention is furture elucidated.

3 story frame structures are taken, the quality of ground floor is 3kg, and the quality of the second layer is 1kg, the quality of third layer It is 2kg, the first stiffness layer is 2kN/m, and the second layer and third layer rigidity are 1kN/m, and damping ratio uses Rayleigh damping C=α M+ β K, wherein, α=0.05, β=0.004, excitation uses white noise arbitrary excitation, and noise level is the 10% of actual signal variance, Sample frequency is 10Hz, and sampled signal is the acceleration at every layer of position of 3 layers of framework.

Specific embodiment is as follows：

(1) sampling obtains vibration acceleration y (t)=[y of three story frame structures₁(t),y₂(t),y₃(t)]^T, select the 3rd The response y of layer₃T () tries to achieve the cross-correlation function matrix r of each components of y (t) as reference signal_y(t)=[r₁₃(t),r₂₃(t), r₃₃(t)]^T, wherein r_ijT () represents y_i(t) and y_jCross-correlation function between (t), i, j=[1,2,3].

(2) to r_yT three cross-correlation functions in () carry out Fast Fourier Transform (FFT) respectively, obtain the complex field number of frequency domain According to R_y(ω), takes R_yThe real part R of (ω)_Re(ω) or imaginary part R_Im(ω)。

(3) by R_Re(ω) or R_Im(ω), using fast independent component analysis method, obtains separating square as analysis object Battle arrayFurther solve vibration shape matrix A=D^-1, obtain normalized vibration shape matrix as follows：

(4) the cross-correlation function matrix r obtained using step (1)_y(t)=[r₁₃(t),r₂₃(t),r₃₃(t)]^TAnd step (3) the separation matrix D for obtaining passes through formula S (t)=Dr_yT () obtains free damped modal response matrix S (t)=[s₁(t), s₂(t),s₃(t)]^T。

(5) to jth rank modal vector s_jT () implements Fast Fourier Transform (FFT), have damping to shake using the pickup of peak extraction method Dynamic frequency ω_0dj, damping ratios ξ is obtained using half-power bandwidth method_0j, wherein j=[1,2,3].

(6) according to step (5) and relational expressionProvide ω_nj、ω_djAnd ζ_jInitial value ω_0nj、 ω_0djAnd ξ_0j, and given α_0j=1,Wherein j=[1,2,3].

(7) estimate of jth rank modal response isThe error of fitting of modal response is E will be minimized as target, and be calculated according to step (6)Initial value, obtained using least-squares iteration method s_jT the optimal estimation of parameter in (), finally gives each rank natural frequency ω_nj, damped frequency ω_djAnd dampingratioζ_j.Result is： ω_n1=0.0452, ω_n2=0.1403, ω_n3=0.2580, ω_d1=0.0451, ω_d2=0.1403, ω_d3=0.2580, ζ₁ =5.5109%, ζ₂=1.7646%, ζ₃=0.9755%.

Claims (1)

1. it is a kind of to damp engineering structure Modal Parameters Identification greatly, it is characterised in that step is as follows：

Step one：Calculate Mode Shape matrix

(1) vibration response signal y (t)=[y of structure is gathered₁(t),y₂(t),…,y_k(t)]^T, wherein k is number of probes；Choosing Fixed a certain signal y_jAs reference, the cross-correlation function matrix r of each components of y (t) is obtained_y(t)；

(2) to r_yT () enters line translation, obtain the plural numeric field data R of frequency domain_y(ω), following form：

R_y(ω)=R_Re(ω)+iR_Im(ω)

Take R_yThe real part R of (ω)_Re(ω) or imaginary part R_Im(ω)；

(3) by R_Re(ω) or R_Im(ω) obtains separation matrix D as analysis object, solves the inverse matrix D of D^-1, obtain vibration shape square Battle array A=D^-1；

(4) according to step (1) and step (3), modal response matrix is calculated：

S (t)=Dr_y(t)

In formula：S (t) is free damped modal response, and S (t)=[s₁(t),s₂(t),…,s_l(t)]^T, D is separation matrix, r_yT () is cross-correlation function matrix, l is rank number of mode；

Step 2：Calculate each rank modal frequency and damping ratio

(5) to jth rank modal vector s_jT () implements conversion, and pick up damping vibrition frequencies omega_0dj, try to achieve damping ratios ζ_0j, wherein j=[1,2 ..., l]；

(6) jth rank modal response s_jT the theoretical expression of () is：

According to step (5) and relational expressionProvide s_jEach parameter ω in (t)_nj、ω_djAnd ζ_jInitial value ω_0nj、ω_0djAnd ζ_0j, and by factor alpha_jAnd phaseInitial value be taken as constant, wherein j=[1,2 ..., l] respectively；

(7) estimate of jth rank modal response is：

Wherein：WithRepresentThe estimate of middle parameters；The error of fitting of modal response For：

$e=\left|\right|{\hat{s}}_j\left(t\right)-s_j\left(t\right)|{|}_2$

Wherein：||·||₂Represent 2- norms；E will be minimized as target, and be calculated according to step (6)Just Initial value, obtains s_jT the optimal estimation of parameter in (), finally gives each rank natural frequency ω_nj, damped frequency ω_djAnd damping ratio ζ_j。